How do you simplify root(3)(3000)3√3000?

1 Answer
Stefan V.
Jul 23, 2015

You check to see if you can find a perfect cube to extract from the cube root.

Explanation:

Since 30003000 is not a perfect cube itself, you're going to have to find a way of writing this number as a product between a perfect cube and another number.

In this case, you can write 30003000 as being

3000 = 1000 * 3 = 100 * 10 * 3 = 10 * 10 * 10 * 3 = 10""^3 * 33000=1000⋅3=100⋅10⋅3=10⋅10⋅10⋅3=103⋅3

This means that the cube root can be simplified as

root(3)(3000) = root(3)(10""^3 * 3)3√3000=3√103⋅3

root(3)(3000) = root(3)(10""^3) * root(3)(3) = color(green)(10 * root(3)(3))3√3000=3√103⋅3√3=10⋅3√3

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